Algebra Examples

$4 x (3 x^{2} + 5 y)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$4 x (3 x^{2}) + 4 x (5 y)$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 3 x \cdot x^{2} + 4 x (5 y)$

Step 1.2.2

Rewrite using the commutative property of multiplication.

$4 \cdot 3 x \cdot x^{2} + 4 \cdot 5 x y$

Step 2

Simplify each term.

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Step 2.1

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 2.1.1

Move $x^{2}$ .

$4 \cdot 3 (x^{2} x) + 4 \cdot 5 x y$

Step 2.1.2

Multiply $x^{2}$ by $x$ .

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Step 2.1.2.1

Raise $x$ to the power of $1$ .

$4 \cdot 3 (x^{2} x^{1}) + 4 \cdot 5 x y$

Step 2.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 3 x^{2 + 1} + 4 \cdot 5 x y$

Step 2.1.3

Add $2$ and $1$ .

$4 \cdot 3 x^{3} + 4 \cdot 5 x y$

Step 2.2

Multiply $4$ by $3$ .

$12 x^{3} + 4 \cdot 5 x y$

Step 2.3

Multiply $4$ by $5$ .

$12 x^{3} + 20 x y$

Step 3

Find the greatest common factor.

$4 x$

Step 4

Find the list of all common factors for $12 x^{3} + 20 x y$ by finding the greatest common factor (GCF) for $12 x^{3} + 20 x y$ and breaking it down to the list of common factors $1, 4, 2, 2, x, 4 x$ . Then find all the possible combinations of these common factors, which are also common factors.

$4 x, 2 x, x, 4, 2, 1$